Automated modulation classification of signals is an extremely useful technique for both military and commercial communications equipment. In non-cooperative communications such as signal surveillance and some cognitive radio applications, the modulation scheme is unknown and has to be estimated and classified automatically. Continuing research and development has led to steady progress and advances in automated modulation classification techniques over the years. However, these techniques still suffer from a number of difficulties and limitations when being implemented in non-cooperative environments in the field, because of unknown parameters such as signal and noise power, carrier frequency and pulse shape, and so on. Those skilled in the art recognize that prior art signal classification equipment, techniques and methods need to be more robust in order to perform adequately in harsh environmental conditions.
One potentially promising technique is the zero-crossing approach, which should be relatively simple to implement, but to date has not yet been successfully accomplished. Recognizing phase-shift-keying (PSK) with a zero-crossing approach has only met with limited success.
A brief examination of the zero-crossing approach in signal repetition rate estimation points to a few of the most noteworthy difficulties with that approach. If we denote f(k), k=1, 2, . . . , as a digitized intermediate frequency (IF) copy of an unknown phase-shifted keying signal at time t(k), then denote a subset of t(k) as x(1), x(2), . . . which are zero-crossing samples of f(k), i.e. f(x(i))=0 for all i, and also denote φ(1), φ(2), . . . as phase symbols of f(k), then one can estimate the relative phase of f(k) at the mth symbol according to this expression:
                              ϕ          ⁡                      (            m            )                          =                  2          ⁢          π          ⁢                                          ⁢                      f            c                    ⁢                                    {                                                1                                      L                    m                                                  ⁢                                                      ∑                                          n                      =                                              j                        m                                                                                                            j                        m                                            +                                              L                        m                                            -                      1                                                        ⁢                                      [                                                                  x                        ⁡                                                  (                          n                          )                                                                    -                                              n                                                  2                          ⁢                                                      f                            c                                                                                                                ]                                                              }                        .                                              Equation        ⁢                                  ⁢                  (          1          )                    where fc is the center frequency of f(k), Lm is the number of zero-crossing samples within the mth symbol period, and x(n), n=jm, jm+1, . . . , jm+Lm−1 are zero-crossing points within the mth symbol time-period. The underlying assumptions are that the symbol rate of f(k) is known, the symbol has a square pulse shape, the symbol timing is perfectly matched and that the center frequency is either previously known or can be estimated accurately. The differential phase of f(k), which is denoted by θ(m), is calculated by:θ(m)=[φ(m)−φ(m−1)] mod(2π)  Equation (2)Then, the phase-shifted keying signal f(k) is classified by correlating the histogram of θ(2), θ(3), . . . , θ(M) with a number of known templates in order to determine the best match.
This prior art approach suffers from a number of drawbacks. The drawbacks include the need to know the center frequency fc accurately in Equation 1 in order to estimate φ(m) and the need to conduct symbol estimation and symbol timing precisely in order to align the starting point x(j) and ending point x(j+Lm−1) within the desired symbol time-period in order to reliably detect zero-crossing points. Another drawback is the lack of reliability in detecting zero-crossing points due to the additive noise. If the zero-crossing points x(i)=t(a) are not detected due to noise, but points x(i+1)=t(b) are still detected in spite of the noise, then x(i)=t(b) will be mistakenly used in Equation 1 and consequently all further phase estimates after time t(a) will also be incorrect. The prior art approach also requires a square pulse shape, and if a square pulse shape is not available, then the zero-crossing points near the pulse edges will be dominated by noise and cause faulty detections. These kinds of limitations of the zero-crossing approach for signal repetition rate estimation devices and techniques along with long-standing prior art difficulties in modulated classification such as questionable strength in the face of harsh environmental conditions have created a long-felt need for a zero-crossing point estimating technique that is faster, more robust and more accurate than current zero-crossing modulation classification techniques. Up until now, there is no available zero-crossing demodulation and classification approach that overcomes the long-standing limitations, shortcomings and disadvantages of the prior art equipment and techniques.